The obvious would be the bulbs are burnt, then look at the fuses for the taillights, and then the wiring. The holders where the lights themselves plug in are bad sometimes; you can get them cheap at a pick-a-part yard.
Most often the tail lights and dash lights share a single feed and fuse. Assuming you have checked the fuses (probably marked as tail or courtesy) then I would next check the head light switch. If you have good fuse and the head light gives a voltage out while in the 'parking light' position (usually between off and headlights) then you need to start chasing wiring. If you need more, post another question, and I'll see if I can walk you further down the path. I had this exact same problem and found out that the headlight switch was just making enough contact with the plug for the headlights to work. We plugged that in and the tail lights and dashboard lights started working also.
I had to get all new tale lights, the switchboards go bad on them. I found mine off craigslist, but u can also find them at a salvage yard.
replace fuse
Problem Solved: The previous owner installed the incorrect tail/turn/stop light bulbs. The bulbs had only one filiment instead of two. All is working perfectly now. Don't go to Walmart to find auto parts. Go to a REAL part store!
My Brake tail Lights Stay on when my car is complete turned off and my lights are off to.
The headlights and the tail lights may not be working on the 1981 El Camino because of a mechanical breakdown.
If your headlights work, but your tail lights don't, your bulbs could be blown. It is possible that you have a shortage in your car.
one of two things, BAD EARTH, or Relay switch.
check the fuses - there is no fuse for the headlights.
Most likely a fuse.
my left tail light does'nt work
Check the ground wire to the tail lights.
If you have no brake lights or tail lights then you've probably got an electrical problem. Check the fuses first and see if you have one or more blown.
my headlights work but my taillights and dash light dont work whats wrong
Fuse, wiring, bulbs
Most likely a fuse or a bad ground.
If your referring to tail lights just turn off your headlights and they will turn off. If your referring to break lights take your foot of the break pedal.